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Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data

Author

Listed:
  • Victor Aguiar

    () (Department of Economics, University of Western Ontario)

  • Roland Pongou

    () (Department of Economics, University of Ottawa)

  • Jean-Baptiste Tondji

    () (Department of Economics, University of Ottawa)

Abstract

We study the Shapley wage function, a wage scheme in which a worker's pay depends both on the number of hours worked and on the output of the firm. We then provide a way to measure the distance of an arbitrary wage scheme to this function in limited datasets. In particular, for a fixed technology and a given supply of labor, this distance is additively decomposable into violations of the classical axioms of efficiency, equal treatment of identical workers, and marginality. The findings have testable implications for the different ways in which popular wage schemes violate basic properties of distributive justice in market organizations. Applications to the linear contract and to other well-known compensation schemes are shown.

Suggested Citation

  • Victor Aguiar & Roland Pongou & Jean-Baptiste Tondji, 2016. "Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data," Working Papers 1613e, University of Ottawa, Department of Economics.
  • Handle: RePEc:ott:wpaper:1613e
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    References listed on IDEAS

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    1. Geoffroy de Clippel & Kareen Rozen, 2013. "Fairness through the Lens of Cooperative Game Theory: An Experimental Approach," Cowles Foundation Discussion Papers 1925, Cowles Foundation for Research in Economics, Yale University.
    2. Khmelnitskaya, Anna B., 1999. "Marginalist and efficient values for TU games," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 45-54, July.
    3. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
    4. Brügemann, Björn & Gautier, Pieter A. & Menzio, Guido, 2015. "Intra Firm Bargaining and Shapley Values," CEPR Discussion Papers 10794, C.E.P.R. Discussion Papers.
    5. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    6. Lars A. Stole & Jeffrey Zwiebel, 1996. "Intra-firm Bargaining under Non-binding Contracts," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 375-410.
    7. Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
    8. Acemoglu, Daron & Hawkins, William B., 2014. "Search with multi-worker firms," Theoretical Economics, Econometric Society, vol. 9(3), September.
    9. L. S. Shapley & Martin Shubik, 1967. "Ownership and the Production Function," The Quarterly Journal of Economics, Oxford University Press, vol. 81(1), pages 88-111.
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    Cited by:

    1. Roland Pongou & Jean-Baptiste Tondji, 2016. "Valuing Inputs Under Supply Uncertainty: The Bayesian Shapley Value," Working Papers 1617E, University of Ottawa, Department of Economics.
    2. repec:eee:gamebe:v:108:y:2018:i:c:p:206-224 is not listed on IDEAS

    More about this item

    Keywords

    Shapley wage function; firm; fairness violations; linear contract; bargaining; limited data;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D20 - Microeconomics - - Production and Organizations - - - General
    • D30 - Microeconomics - - Distribution - - - General
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General

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